1. Field of the Invention
This invention relates to leapfrog filter, and more particularly it pertains to such a filter which is so designed as to be easy to adjust the pass band width thereof and less likely to produce in-band ripple.
2. Description of the Prior Art
Referring to FIG. 1, description will first be made of an example of conventional active filter, which is constructed in the form of biquad circuit constituting a low-pass filter. The transfer function T(S) of a common low-pass filter is given as follows: ##EQU1## where .omega..sub.0 is angular frequency; s is complex variable; Q is quality factor; and H is gain factor.
The relationship between input and output voltages V.sub.1 and V.sub.2 of the biquad circuit can be expressed in the form of transfer function T(S) as follows: ##EQU2##
Assuming that the factor of each term in Equation (1) and that in Equation (2) are equal to each other, the angular frequency .omega..sub.0 is given as follows: EQU .omega..sub.0.sup.2 =1/R.sub.20 R.sub.40 C.sub.10 C.sub.20
Further, since the angular frequency .omega..sub.0 is given as .omega..sub.0 =2.pi.F.sub.0, the center frequency f.sub.0 can be expressed as follows: EQU f.sub.0 =1/2.pi..multidot..sqroot.R.sub.20 R.sub.40 C.sub.10 C.sub.20 ( 3)
Still further, from the Equations (1) and (2), the quality factor can be expressed as follows: EQU Q=.sqroot.R.sub.10.sup.2 C.sub.10 /R.sub.20 R.sub.40 C.sub.20 ( 4)
As will be seen from Equation (3), it is required that circuit constants such as resistors R.sub.20 and R.sub.40 or capacitors C.sub.10 and C.sub.20 be made variable in an attempt to make variable the center frequency f.sub.0. Thus, to make variable the center frequency f.sub.0, the conventional biquad circuit requires externally mounted components such as the resistors R.sub.20 and R.sub.40 or capacitors C.sub.10 and C.sub.20 which are unsuitable for semiconductor integrated circuit fabrication. With the conventional biquad circuit, it is required that constants such as resistors R.sub.20 and R.sub.20 or capacitors C.sub.10 and C.sub.20 be changed when it is attempted to provide the desired center frequency f.sub.0. As will be noted from Equation (4), however, the quality factor Q is also changed by adjusting the externally mounted components, and this requires that the other circuit constants be also changed.
Furthermore, the conventional active filter such as shown in FIG. 1 is disadvantageous in that the manufacturing cost is high because a number of electronic components are mounted onto a printed circuit board. Another disadvantage is such that when it is attempted to adjust the center frequency f.sub.0 of the filter, it is required that such adjustment be effected with components having the circuit constants thereof set at predetermined values being mounted on the printed circuit board, and this inevitably increases the number of steps for band-width adjustment and assembling of the filter.